P&S: Gibbs? Clifford!

Abstract

Der Bereich Praktika, Projekte, Seminare umfasst Lehrveranstaltungen in unterschiedlichen Formaten zum Erwerb von praktischen Kenntnissen und Fertigkeiten. Ausserdem soll selbstständiges Experimentieren und Gestalten gefördert, exploratives Lernen ermöglicht und die Methodik von Projektarbeiten vermittelt werden.

Objective

Python, an interpreted, high-level programming language, has arguably become the de facto standard for exploratory, interactive, and computation-driven scientific research. Free and universally available, Python comes prepackaged with a wealth of general-purpose libraries, popularizing the notion that it comes with “batteries included.” Geometric Algebra, based on the algebra of multivectors introduced by Clifford in1878 and applied to the mathematical description of physics by Hestenes a century later, is a revelation, like the sun making its way through the fog: the Gibb’s cross product in R^3 with its troubling sides is merged into the more general vector product (inner and outer product) so that e.g. the electromagnetic field in the Maxwell equations as well as the imaginary unit in quantum mechanics suddenly acquire another (and hopefully more limpid) meaning. Objective of this practical course is to introduce the students to the power of Python by making them discover geometric algebra. Each of the seven sessions begins with an introduction about a geometric algebra aspect (first 2 h) followed by corresponding exercises in Python (second 2 h). Students are thus expected to bring their own laptop for the activity with Python! Attendance is compulsory for at least five out of the seven afternoons. Students divided in subgroups will be required to submit two homeworks (~15 h each), mandatory to earn the two credit points! Dates: Wed 25.2, 4.3, 11.3, 18.3, 25.3, 1.4, 15.4 (14:15-18:00)

Resources